Valeriy Ivanovich Zakamulin

• Giner, Javier & Zakamulin, Valeriy Ivanovich (2026). Analytical solutions to state transition probabilities in a semi-markov model. Decisions in Economics and Finance (DAF). ISSN 1593-8883. 49, p. 869–912. doi: 10.1007/s10203-026-00573-w. Full text in Research Archive Show summary

  Semi-Markov models provide a more realistic framework for modeling and forecasting real-world processes than conventional Markov models. However, their practical use is severely constrained by the lack of analytical tractability. This paper proposes a viable and tractable alternative based on an expanded-state Markov model with a specific topological structure. We show that the proposed semi-Markov model remains analytically tractable when the process consists of two semi-Markovian states, each represented by at least three Markovian sub-states. Closed-form expressions for the state transition probabilities are derived for both discrete- and continuous-time settings. Empirical analysis using long-term data on U.S. business and stock market cycles demonstrates that the proposed model provides a statistically superior fit compared to conventional Markov models, underscoring its practical relevance and effectiveness.

• Zakamulin, Valeriy Ivanovich (2026). Calendar anomalies: Real patterns or data-mining artifacts? The North American journal of economics and finance. ISSN 1062-9408. 85. doi: 10.1016/j.najef.2026.102653. Full text in Research Archive Show summary

  This paper reexamines well-known calendar anomalies in equity returns with the objective of determining whether these effects are genuine return regularities or artifacts of data mining. We study four canonical anomaly families—the day-of-the-week, week-of-the month, month-of-the-year (January), and Sell-in-May effects—using U.S. equity data, and we also evaluate international evidence for the Sell-in-May effect. Our methodology explicitly accounts for the selection inherent in the discovery of calendar anomalies by applying data-mining-adjusted bootstrap tests that mimic a researcher’s within-family search across alternative calendar definitions. Our results show that, after correcting for data mining, the day-of-the-week, week-of-the-month, and month-of-the-year anomalies remain statistically significant in the full sample, with the strongest evidence coming from the earlier part of the sample, indicating that these effects were not merely statistical artifacts. At the same time, we find that these anomalies largely disappear in later subsamples beginning in the early 1990s. In contrast, the Sell-in-May effect proves more resilient: international evidence remains robust to data-mining concerns. Overall, the findings suggest that several calendar anomalies were real features of historical return data, even though their economic relevance has diminished in more recent decades.

• Zakamulin, Valeriy Ivanovich (2025). Behavioral Origins of Implied Volatility: Loss Aversion and Risk Asymmetry. Journal of Behavorial Finance. ISSN 1542-7560. doi: 10.1080/15427560.2025.2528040. Full text in Research Archive Show summary

  This article investigates whether loss aversion and domain-specific risk attitudes—absent probability distortion—can explain key features of implied volatility: the smirk, its term structure, and volatility and skewness risk premia. We use an equilibrium pricing framework with a representative investor who maximizes a flexible behavioral utility function that separately evaluates gains and losses. Our results show that the observed patterns can emerge even under normally distributed returns. Importantly, our results indicate that neither loss aversion nor asymmetric risk preferences alone are sufficient to explain the implied volatility smirk. Rather, the smirk arises from the interaction between the two.

• Zakamulin, Valeriy Ivanovich (2024). Transaction Cost Optimization in a Fully Invested Portfolio with Target Weights. Journal of Investing. ISSN 1068-0896. 34(1), p. 38–57. doi: 10.3905/joi.2024.1.328. Full text in Research Archive
• Zakamulin, Valeriy Ivanovich & Giner, Javier (2024). Optimal trend-following rules in two-state regime-switching models. Journal of Asset Management. ISSN 1470-8272. doi: 10.1057/s41260-024-00357-0. Full text in Research Archive
• Zakamulin, Valeriy Ivanovich (2024). Stock price overreaction: evidence from bull and bear markets. Review of Behavioral Finance. ISSN 1940-5979. doi: 10.1108/RBF-03-2024-0088. Full text in Research Archive
• Zakamulin, Valeriy Ivanovich (2023). A New Predictability Pattern in the US Stock Market Returns. Journal of Portfolio Management. ISSN 0095-4918. 49(3), p. 169–183. doi: 10.3905/jpm.2022.1.437. Full text in Research Archive Show summary

  This article documents a new stock market anomaly that seems to have escaped the attention of both investment professionals and academics. For more than a century, the monthly market return has been predicted by the monthly market return at lag 5. This predictability is marketwide and is most evident in the returns of portfolios of large and growth stocks. The trading strategy incorporating this predictability yields superior performance that cannot be attributed to common risk factors. A closer investigation of the new anomaly reveals that not each calendar month possesses predictive ability. Therefore, there is a link between the new anomaly and calendar effects in stock returns.

• Giner, Javier & Zakamulin, Valeriy Ivanovich (2023). A regime-switching model of stock returns with momentum and mean reversion. Economic Modelling. ISSN 0264-9993. 122. doi: 10.1016/j.econmod.2023.106237. Full text in Research Archive Show summary

  A vast body of empirical literature documents the existence of short-term momentum and medium-term mean reversion in various financial markets. However, few theoretical models explain these two common phenomena. A Markov model, wherein the return process randomly switches between bull and bear states, can reproduce many stylized facts of financial asset returns, excluding the mean reversion. An important limitation of the Markov model is that the state termination probability does not depend on age. We develop a semi-Markov model wherein, following the empirical evidence, the state termination probability increases with age. We demonstrate that this model induces short-term return momentum and subsequent reversal. We calibrate our model to real-world data and show that the empirical results agree with our theoretical model.

• Zakamulin, Valeriy Ivanovich & Giner, Javier (2023). Optimal trend-following with transaction costs. International Review of Financial Analysis. ISSN 1057-5219. 90, p. 1–17. doi: 10.1016/j.irfa.2023.102928. Full text in Research Archive Show summary

  Despite the widespread popularity of trend-following investing, optimal trend-following in the presence of transaction costs remains poorly understood. Existing studies on the subject are limited and rely on intricate theoretical models, posing great challenges in practical applications. In this paper, we propose a new, more pragmatic model that balances theoretical simplicity and practical relevance. Under plausible assumptions regarding the trend dynamics, we establish a noteworthy resemblance between the optimal trend-following strategy and the well-known simple moving average crossover rule. Consequently, our model provides a compelling rationale for the practical adoption of crossover rules. We also perform historical simulations that demonstrate the effectiveness of our model, supporting our theoretical findings. In short, our paper provides a practical and effective solution to the problem of optimal trend-following with transaction costs.

• Zakamulin, Valeriy Ivanovich (2023). Not all bull and bear markets are alike: insights from a five-state hidden semi-Markov model. Risk Management: An International Journal. ISSN 1460-3799. 25(1). doi: 10.1057/s41283-022-00112-y. Full text in Research Archive Show summary

  This paper employs the hidden semi-Markov model and a novel model selection procedure to determine different regimes in the US stock market. The empirical results suggest that the US stock market is switching between five states that can be classified into three bull states and two bear states. The three bull states are categorized as a low-volatility bull market, a high-volatility bull market, and a stock market bubble. One of the bear states represents a regular bear market, while the other corresponds to either a stock market crash or a market correction. The paper demonstrates that the five-state model is consistent with a number of stylized facts and provides many valuable insights into the regime-switching dynamics of the US stock market and the risk-reward pattern of each regime. Besides, the paper demonstrates that the five-state model enables investors to make better asset allocation decisions. Specifically, in out-of-sample tests, the asset allocation strategy based on the five-state model achieves higher performance with lower risk than the strategy based on the two-state model and the buy-and-hold benchmark.

• Zakamulin, Valeriy (2022). Revisiting the duration dependence in the US stock market cycles. Applied Economics. ISSN 0003-6846. doi: 10.1080/00036846.2022.2089344. Full text in Research Archive Show summary

  There is a big controversy among both investment professionals and academics regarding how the termination probability of a market state depends on its age. Using more than two centuries of data on the broad US stock market index, we revisit the duration dependence in bull and bear markets. Our results suggest that the duration dependence for both bull and bear markets is a nonlinear function of the state age. It appears that the duration dependence in bear markets is strictly positive. For 93% of the bull markets, the duration dependence is also positive. Only about 7% of the bull markets, those with the longest durations, do not exhibit positive duration dependence. We also compare a few selected theoretical distributions on their ability to describe the duration dependence in bull and bear markets. Our results advocate that the gamma distribution most often provides the best fit for both the survivor and hazard functions of bull and bear markets. However, our results reveal that none of the selected distributions accurately describes the right tail of the hazard functions.

• Zakamulin, Valeriy & Giner, Javier (2022). Time series momentum in the US stock market: Empirical evidence and theoretical analysis. International Review of Financial Analysis. ISSN 1057-5219. 82. doi: 10.1016/j.irfa.2022.102173. Full text in Research Archive Show summary

  There is much controversy in the academic literature on the presence of short-term trends in financial markets and the trend-following strategy’s profitability. We restrict our attention to studying the time series momentum in the S&P Composite stock price index. Our contributions are both empirical and theoretical. On the empirical side, we present compelling evidence of the presence of short-term momentum. For the first time, we suppose that the returns follow a -order autoregressive process and evaluate this process’s parameters. On the theoretical side, we develop a tractable theoretical model that contributes to our fundamental understanding of the trend-following strategy’s risk, return, and performance. Using our model, we also estimate the power of statistical tests on the trend-following strategy’s profitability and find that these tests suffer from the low power problem.

• Koekebakker, Steen & Zakamulin, Valeriy (2021). Warren Buffett versus Zvi Bodie: Should You Buy Or Sell Put Options? The journal of wealth management. ISSN 1534-7524. 24(2), p. 65–81. doi: 10.3905/jwm.2021.1.137. Full text in Research Archive
• Li, Xingyi & Zakamulin, Valeriy (2020). Stock volatility predictability in bull and bear markets. Quantitative finance (Print). ISSN 1469-7688. doi: 10.1080/14697688.2020.1725101. Full text in Research Archive
• Zakamulin, Valeriy & Hunnes, John A. (2020). Stock earnings and bond yields in the US 1871–2017 : The story of a changing relationship. Quarterly Review of Economics and Finance. ISSN 1062-9769. 79, p. 182–197. doi: 10.1016/j.qref.2020.05.013. Full text in Research Archive
• Zakamulin, Valeriy & Giner, Javier (2020). Trend following with momentum versus moving averages: a tale of differences. Quantitative finance (Print). ISSN 1469-7688. 20(6), p. 985–1007. doi: 10.1080/14697688.2020.1716057. Full text in Research Archive
• Zakamulin, Valeriy (2019). Volatility Weighting over Time in the Presence of Transaction Costs. The journal of wealth management. ISSN 1534-7524. 21(4), p. 33–45. doi: 10.3905/jwm.2019.21.4.033. Full text in Research Archive
• Li, Xingyi & Zakamulin, Valeriy (2019). The term structure of volatility predictability. International Journal of Forecasting. ISSN 0169-2070. doi: 10.1016/j.ijforecast.2019.08.010. Full text in Research Archive
• Zakamulin, Valeriy (2018). Revisiting the Profitability of Market Timing with Moving Averages. International Review of Finance. ISSN 1369-412X. 18(2), p. 317–327. doi: 10.1111/irfi.12132. Full text in Research Archive
• Zakamulin, Valeriy (2017). Superiority of optimized portfolios to naive diversification: Fact or fiction? Finance Research Letters. ISSN 1544-6123. 22, p. 122–128. doi: 10.1016/j.frl.2016.12.007. Full text in Research Archive
• Zakamulin, Valeriy (2017). Secular Mean Reversion and Long-Run Predictability of the Stock Market. Bulletin of Economic Research. ISSN 0307-3378. 69(4), p. 66–93. doi: 10.1111/boer.12105. Full text in Research Archive
• Zakamulin, Valeriy (2016). Optimal dynamic portfolio risk management. Journal of Portfolio Management. ISSN 0095-4918. 43(1), p. 85–99. doi: 10.3905/jpm.2016.43.1.085. Full text in Research Archive
• Zakamulin, Valeriy (2015). A test of covariance-matrix forecasting methods. Journal of Portfolio Management. ISSN 0095-4918. 41(3), p. 97–108. doi: 10.3905/jpm.2015.41.3.097. Full text in Research Archive
• Zakamulin, Valeriy (2014). Predictable Dynamics in the Small Stock Premium. Economics Research International. ISSN 2090-2123. doi: 10.1155/2014/405231. Full text in Research Archive
• Zakamulin, Valeriy (2014). Dynamic Asset Allocation Strategies Based on Unexpected Volatility. The Journal of Alternative Investments. ISSN 1520-3255. 16(4), p. 37–50. doi: 10.3905/jai.2014.16.4.037. Full text in Research Archive
• Zakamulin, Valeriy (2014). The real-life performance of market timing with moving average and time-series momentum rules. Journal of Asset Management. ISSN 1470-8272. 15(4), p. 261–278. doi: 10.1057/jam.2014.25. Full text in Research Archive
• Zakamulin, Valeriy (2014). Portfolio performance evaluation with loss aversion. Quantitative finance (Print). ISSN 1469-7688. 14(4), p. 699–710. doi: 10.1080/14697688.2011.620978. Full text in Research Archive
• Andresen, Arne; Benth, Fred Espen; Koekebakker, Steen & Zakamulin, Valeriy (2014). The CARMA interest rate model. International Journal of Theoretical and Applied Finance. ISSN 0219-0249. 17(2). doi: 10.1142/S0219024914500083. Full text in Research Archive Show summary

  In this paper, we present a multi-factor continuous-time autoregressive moving-average (CARMA) model for the short and forward interest rates. This model is able to present an adequate statistical description of the short and forward rate dynamics. We show that this is a tractable term structure model and provides closed-form solutions to bond prices, yields, bond option prices, and the term structure of forward rate volatility. We demonstrate the capabilities of our model by calibrating it to a panel of spot rates and the empirical volatility of forward rates simultaneously, making the model consistent with both the spot rate dynamics and forward rate volatility structure.

• Zakamulin, Valeriy (2013). Forecasting the size premium over different time horizons. Journal of Banking & Finance. ISSN 0378-4266. 37(3), p. 1061–1072. doi: 10.1016/j.jbankfin.2012.11.006. Full text in Research Archive
• Cogneau, Philippe & Zakamulin, Valeriy (2013). Block bootstrap methods and the choice of stocks for the long run. Quantitative finance (Print). ISSN 1469-7688. 13(9), p. 1443–1457. doi: 10.1080/14697688.2012.713115. Full text in Research Archive
• Zakamouline, Valeri (2011). Sharpe (Ratio) Thinking about the Investment Opportunity Set and CAPM Relationship. Economics Research International. ISSN 2090-2123. 2011. doi: 10.1155/2011/781760. Full text in Research Archive
• Zakamouline, Valeri (2011). The Performance Measure You Choose Influences the Evaluation of Hedge Funds. Journal of Performance Measurement. ISSN 1522-8746. 15(3), p. 48–64. doi: 10.2139/ssrn.1403246. Full text in Research Archive Show summary

  It is widely accepted that, when return distributions are non-normal, the use of the Sharpe ratio can lead to misleading conclusions. It is well documented that deviations of hedge fund return distributions from normality are statistically significant. The literature on performance evaluation that takes into account the non-normality of return distributions is a vast one. However, there is another stream of research that advocates that the choice of performance measure does not influence the evalutaion of hedge funds.

• Zakamouline, Valeri (2010). Are There Long Cycles in the U.S. Stock Market? In Knudsen, Jon Paschen & Sødal, Sigbjørn Reidar (Ed.), Økonomi og tid : 18 essays i Pufendorf-tradisjon : festskrift til professor Arild Sæther på 70-årsdagen, 8. august 2010. Fagbokforlaget. ISSN 9788245010244. p. 145–161. Full text in Research Archive
• Zakamouline, Valeri (2010). On the Consistent Use of VaR in Portfolio Performance Evaluation: A Cautionary Note. Journal of Portfolio Management. ISSN 0095-4918. 37(1), p. 92–104. doi: 10.3905/jpm.2010.37.1.092. Full text in Research Archive Show summary

  The portfolio performance measures based on the Value at Risk (VaR) concept have gained widespread popularity and are often used in empirical studies. In the majority of empirical studies, however, a VaR-based performance measure is inconsistently used. In this article, Zakamouline emphasizes how to consistently use VaR in portfolio performance evaluation. He also elaborates on a simple framework that allows the derivation of a general formula for a portfolio performance measure that is not limited to the use of VaR-based reward and risk measures, but is valid for all reward and risk measures that satisfy a few plausible properties

• Benth, Fred Espen; Koekebakker, Steen & Zakamouline, Valeri (2010). A Continuous Time Model for Interest Rate with Autoregressive and Moving Average Components. AIP Conference Proceedings. ISSN 0094-243X. 1281, p. 531–534. doi: 10.1063/1.3498530. Full text in Research Archive
• Zakamulin, Valeriy & Koekebakker, Steen (2009). A generalisation of the mean-variance analysis. European Financial Management. ISSN 1354-7798. 15(5), p. 934–970. Full text in Research Archive
• Zakamouline, Valeri (2009). Option Pricing and Hedging in the Presence of Transaction Costs and Nonlinear Partial Differential Equations. In Catlere, Patrick N. (Eds.), book ?Financial Hedging? edited by Patrick N. Catlere. Nova Science Publishers. ISSN 9781606926659. p. -–-. Full text in Research Archive
• Zakamouline, Valeri (2009). The Best Hedging Strategy in the Presence of Transaction Costs. International Journal of Theoretical and Applied Finance. ISSN 0219-0249. 12(6). Full text in Research Archive Show summary

  Considerable theoretical work has been devoted to the problem of option pricing and hedging with transaction costs. A variety of methods have been suggested and are currently being used for dynamic hedging of options in the presence of transaction costs. However, very little was done on the subject of an empirical comparison of different methods for option hedging with transaction costs. In a few existing studies the different methods are compared by studying their empirical performances in hedging only a plain-vanilla short call option. The reader is tempted to assume that the ranking of the different methods for hedging any kind of option remains the same as that for a vanilla call. The main goal of this paper is to show that the ranking of the alternative hedging strategies depends crucially on the type of the option position being hedged and the risk preferences of the hedger. In addition, we present and implement a simple optimization method that, in some cases, improves considerably the performance of some hedging strategies

• Zakamouline, Valeri & Koekebakker, Steen (2009). Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance. Journal of Banking & Finance. ISSN 0378-4266. 33(7), p. 1242–1254. doi: 10.1016/j.jbankfin.2009.01.005. Full text in Research Archive Show summary

  This paper presents a theoretically sound portfolio performance measure that takes into account higher moments of distribution. This measure is motivated by a study of the investor's preferences to higher moments of distribution within Expected Utility Theory and an approximation analysis of the optimal capital allocation problem. We show that this performance measure justifies the notion of the Generalized Sharpe Ratio (GSR) introduced by Hodges (1998). We present two methods of practical estimation of the GSR: nonparametric and parametric. For the implementation of the parametric method we derive a closed-form solution for the GSR where the higher moments are calibrated to the normal inverse Gaussian distribution. We illustrate how the GSR can mitigate the shortcomings of the Sharpe ratio in resolution of Sharpe ratio paradoxes and reveal the real performance of portfolios with manipulated Sharpe ratios. We also demonstrate the use of this measure in the performance evaluation of hedge funds. (C) 2009 Elsevier B.V. All rights reserved.

• Zakamouline, Valeri & Koekebakker, Steen (2009). A Generalisation of the Mean-Variance Analysis. European Financial Management. ISSN 1354-7798. 15(5), p. 934–970. doi: 10.1111/j.1468-036X.2009.00483.x. Full text in Research Archive Show summary

  In this paper we consider a decision maker whose utility function has a kink at the reference point with different functions below and above this reference point. We also suppose that the decision maker generally distorts the objective probabilities. First we show that the expected utility function of this decision maker can be approximated by a function of mean and partial moments of distribution. This 'mean-partial moments' utility generalises not only mean-variance utility of Tobin and Markowitz, but also mean-semivariance utility of Markowitz. Then, in the spirit of Arrow and Pratt, we derive an expression for a risk premium when risk is small. Our analysis shows that a decision maker in this framework exhibits three types of aversions: aversion to loss, aversion to uncertainty in gains, and aversion to uncertainty in losses. Finally we present a solution to the optimal capital allocation problem and derive an expression for a portfolio performance measure which generalises the Sharpe and Sortino ratios. We demonstrate that in this framework the decision maker's skewness preferences have first-order impact on risk measurement even when the risk is small.

• Zakamouline, Valeri (2008). Option Pricing and Hedging in the Presence of Transaction Costs and Nonlinear Partial Differential Equations, ``Nonlinear Models in Mathematical Finance: Research Trends in Option Pricing" edited by Matthias Ehrhardt. Nova Science Publishers, Inc.. Full text in Research Archive Show summary

  In the presence of transaction costs the perfect option replication is impossible which invalidates the celebrated Black and Scholes (1973) model. In this chapter we consider some approaches to option pricing and hedging in the presence of transaction costs. The distinguishing feature of all these approaches is that the solution for the option price and hedging strategy is given by a nonlinear partial differential equation (PDE). We start with a review of the Leland (1985) approach which yields a nonlinear parabolic PDE for the option price, one of the first such in finance. Since the Leland's approach to option pricing has been criticized on different grounds, we present a justification of this approach and show how the performance of the Leland's hedging strategy can be improved. We extend the Leland's approach to cover the pricing and hedging of options on commodity futures contracts, as well as path-dependent and basket options. We also present examples of finite-difference schemes to solve some nonlinear PDEs. Then we proceed to the review of the most successful approach to option hedging with transaction costs, the utility-based approach pioneered by Hodges and Neuberger (1989). Judging against the best possible tradeoff between the risk and the costs of a hedging strategy, this approach seems to achieve excellent empirical performance. The asymptotic analysis of the option pricing and hedging in this approach reveals that the solution is also given by a nonlinear PDE. However, this approach has one major drawback that prevents the broad application of this approach in practice, namely, the lack of a closed-form solution. The numerical computations are cumbersome to implement and the calculations of the optimal hedging strategy are time consuming. Using the results of asymptotic analysis we suggest a simplified parameterized functional form of the optimal hedging strategy for either a single option or a portfolio of options and a method for finding the optimal parameters.

• Zakamouline, Valeri (2008). Hedging of Option Portfolios and Options on Several Assets with Transaction Costs and Nonlinear Partial Differential Equations. International Journal of Contemporary Mathematical Sciences. ISSN 1312-7586. 3(4), p. 159–180. Full text in Research Archive Show summary

  The knowledge of the Leland's hedging strategy is important for optimal hedging of options and option portfolios in the presence of transaction costs. In this paper we extend the Leland's (1985) option pricing and hedging method to cover the cases of pricing and hedging of a portfolio of options on a futures contract, a portfolio of strongly path-dependent options on a stock, and options on several assets. In all the cases as a result we obtain a nonlinear partial differential equation for the option portfolio price. Generally, these nonlinear partial differential equations must be solved numerically and we present some examples of finite difference schemes to solve them. The ultimate practical goal, however, is not the solution for the option portfolio price, but the solution for the values of the Leland's hedging delta. We illustrate the advantages of the Leland's hedging strategy against the Black-Scholes hedging strategy.

• Zakamouline, Valeri (2007). On the Pricing and Hedging of Options on Commodity Forward and Futures Contracts. A Note. The Icfai Journal of Derivatives Markets. ISSN 0972-9119. 4(2), p. 6–21. Full text in Research Archive Show summary

  In recent years there appeared some organized markets for forward contracts and options on these contracts. In this paper we review briefly the organization of trade on a centralized forward market. Assuming a friction-free market with constant interest rate we build a consistent continuous time framework for the valuation and hedging of options on a forward or a futures contract. This framework takes into account the peculiarities of a forward/futures contract. In our framework we consider the pricing and hedging of options on a forward contract and reconsider the Black-76 model for the pricing and hedging of options on a futures contract.

• Zakamouline, Valeri (2006). European option pricing and hedging with both fixed and proportional transaction costs. Journal of Economic Dynamics and Control. ISSN 0165-1889. 30(1), p. 1–25. Full text in Research Archive Show summary

  In this paper we provide a systematic treatment of the utility based option pricing and hedging approach in markets with both fixed and proportional transaction costs: we extend the framework developed by Davis et al. (SIAM J. Control Optim., 31 (1993) 470) and formulate the option pricing and hedging problem. We propose and implement a numerical procedure for computing option prices and corresponding optimal hedging strategies. We present a careful analysis of the optimal hedging strategy and elaborate on important differences between the exact hedging strategy and the asymptotic hedging strategy of Whalley and Wilmott (RISK 7 (1994) 82). We provide a simulation analysis in order to compare the performance of the utility based hedging strategy against the asymptotic strategy and some other common strategies. (c) 2004 Elsevier B.V. All rights reserved.

• Zakamouline, Valeri (2006). Efficient analytic approximation of the optimal hedging strategy for a European call option with transaction costs. Quantitative finance (Print). ISSN 1469-7688. 6(5), p. 435–445. Full text in Research Archive Show summary

  One of the most successful approaches to option hedging with transaction costs is the utility-based approach, pioneered by Hodges and Neuberger [Rev. Futures Markets, 1989, 8, 222?239]. Judging against the best possible trade-off between the risk and the costs of a hedging strategy, this approach seems to achieve excellent empirical performance. However, this approach has one major drawback that prevents the broad application of this approach in practice: the lack of a closed-form solution. We overcome this drawback by presenting a simple yet efficient analytic approximation of the solution. We provide an empirical testing of our approximation strategy against the asymptotic and some other well-known strategies and find that our strategy outperforms all the others.

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• Zakamulin, Valeriy Ivanovich & Giner, Javier (2025). The Ultimate Moving Average Handbook: Bringing Science into the Art of Trend Following. Palgrave Macmillan. ISBN 9783031909061. 570 p. doi: 10.1007/978-3-031-90907-8. Full text in Research Archive Show summary

  In this book, the authors propose a quantitative assessment of the properties of trend-following rules based on moving averages. They argue that there are three primary properties of trend-following rules: responsiveness, smoothness, and accuracy. Given the prevalent claims that each exotic moving average offers superior responsiveness and smoothness compared to prior versions, the book provides a means to verify the accuracy of these assertions. It offers systematic and comprehensive coverage of various types of moving averages and the trend-following rules based on moving averages, and focuses on identifying the most crucial properties of trend-following rules and proposing quantitative metrics for their evaluation.

• Zakamulin, Valeriy (2017). Market Timing with Moving Averages: The Anatomy and Performance of Trading Rules. Palgrave Macmillan. ISBN 9783319609690. 278 p. Full text in Research Archive Show summary

  This book provides a comprehensive guide to market timing using moving averages. Part I explores the foundations of market timing rules, presenting a methodology for examining how the value of a trading indicator is computed. Using this methodology the author then applies the computation of trading indicators to a variety of market timing rules to analyse the commonalities and differences between the rules. Part II goes on to present a comprehensive analysis of the empirical performance of trading rules based on moving averages.

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• Zakamulin, Valeriy & Giner, Javier (2022). A Semi-Markov Model for Stock Returns with Momentum and Mean-Reversion. Full text in Research Archive
• Zakamulin, Valeriy (2019). Stock Earnings and Bond Yields in the US 1871 - 2017: A Structural Break Analysis. Full text in Research Archive
• Zakamulin, Valeriy (2018). Abnormal Stock Market Returns around Peaks in VIX: The Evidence of Investor Overreaction? Full text in Research Archive
• Zakamulin, Valeriy (2018). The Limits to Volatility Predictability: Quantifying Forecast Accuracy Across Horizons. Full text in Research Archive
• Zakamulin, Valeriy (2018). The Limits to Volatility Predictability: Quantifying Forecast Accuracy Across Horizons. Full text in Research Archive
• Zakamulin, Valeriy (2017). Abnormal Stock Market Returns around Peaks in VIX: The Evidence of Investor Overreaction? Full text in Research Archive
• Zakamulin, Valeriy (2016). A Comprehensive Look at the Empirical Performance of Moving Average Trading Strategies. Full text in Research Archive
• Zakamulin, Valeriy (2016). Abnormal Stock Market Returns around Peaks in VIX: The Evidence of Investor Overreaction? Full text in Research Archive
• Zakamulin, Valeriy (2015). Optimal Dynamic Portfolio Risk Management. Full text in Research Archive
• Zakamulin, Valeriy (2015). Market Timing with Moving Averages: Anatomy and Performance of Trading Rules. Full text in Research Archive
• Zakamulin, Valeriy (2014). Dynamic Asset Allocation Strategies Based on Unexpected Volatility. Full text in Research Archive
• Zakamulin, Valeriy (2014). The Role of Covariance Matrix Forecasting Method in the Performance of Minimum-Variance Portfolios. Full text in Research Archive
• Zakamulin, Valeriy (2013). Secular Mean Reversion and Long-Run Predictability of the Stock Market. Full text in Research Archive
• Zakamulin, Valeriy (2013). The Real-Life Performance of Market Timing with Moving Average and Time-Series Momentum Rules. Full text in Research Archive
• Zakamulin, Valeriy (2013). Secular Mean Reversion and Long-Run Predictability of the Stock Market. Full text in Research Archive
• Zakamulin, Valeriy (2012). Predicting the Small Stock Premium. Full text in Research Archive
• Zakamulin, Valeriy (2012). Risk Models and their Effect on Performance. Full text in Research Archive
• Zakamulin, Valeriy (2012). Forecasting the Size Premium. Full text in Research Archive
• Zakamouline, Valeri (2012). Predicting the Small Stock Premium Over Different Horizons: What Do We Learn About Its Source? Full text in Research Archive
• Zakamouline, Valeri (2011). Explaining the Dynamics of the Size Premium. Full text in Research Archive
• Zakamouline, Valeri (2011). Long-Term Mean Reversion and Predictability of the U.S. Stock Market Returns. Full text in Research Archive
• Zakamouline, Valeri (2011). Firm Size and Cyclical Variations in Stock Returns: Some Further Evidence. Full text in Research Archive
• Zakamouline, Valeri (2010). Medium-Term Cycles in the U.S. Stock Market and the Size and Value Premiums. Full text in Research Archive
• Zakamouline, Valeri (2010). The Choice of Performance Measure Does Influence the Evaluation of Hedge Funds. Full text in Research Archive
• Zakamouline, Valeri; Koekebakker, Steen & Benth, Fred Espen (2010). A Continuous Time Model for Interest Rate with Autoregressive and Moving Average Components. Full text in Research Archive
• Zakamouline, Valeri (2009). Rational Measures of Portfolio Performance. Full text in Research Archive
• Zakamouline, Valeri (2008). Coherent Measures of Portfolio Performance. Full text in Research Archive
• Zakamouline, Valeri (2008). Accounting for Skewness Preferences in Investment Decisions. Full text in Research Archive
• Zakamouline, Valeri (2008). Analysis of Financial Decision-Making with Loss Aversion. Full text in Research Archive
• Zakamouline, Valeri (2008). Analysis of Financial Decision-Making with Loss Aversion. Full text in Research Archive
• Koekebakker, Steen & Zakamouline, Valeri (2008). Can we measure portfolio performance? ?. 9(1), p. 63–67. Full text in Research Archive
• Zakamouline, Valeri (2008). A Generalization of Mean-Variance Analysis. Full text in Research Archive
• Zakamouline, Valeri (2007). Generalized Sharpe Ratios and Portfolio Performance Evaluation. Full text in Research Archive
• Zakamouline, Valeri (2007). Generalizing the Vasicek Interest Rate Model - A Continuous Time ARMA Approach. Full text in Research Archive
• Koekebakker, Steen & Zakamouline, Valeri (2007). Svar på DnB NOR Markets' metodekritikk. Praktisk Økonomi & Finans. ISSN 1501-0074. 4(bare elektronisk ver). Full text in Research Archive Show summary

  DnB NOR Markets er kritiske til metoden som benyttes i Koekebakker og Zakamouline (2007) og foreslår et alternativ. Her diskuterer vi vår metode og sammenholder det alternative forslaget. Kort oppsummert er DnB NORs metode upassende for investorer med lang investeringshorisont. Den umuliggjør en enkel sammenligning med fornuftige plasseringsalternativer. Avkastningen vektes over tid i henhold til hvor mange produkter som til enhver tid tilbys i markedet. DnB NOR Markets¿ metode virker uegnet til å vurdere historisk avkastning på garanterte spareprodukter, og vi fastholder vårt opprinnelige valg av metode.

• Koekebakker, Steen & Zakamouline, Valeri (2007). Svar på metodekritikk fra DnBNOR markets. Praktisk Økonomi & Finans. ISSN 1501-0074. (web-publisering). Full text in Research Archive
• Koekebakker, Steen & Zakamouline, Valeri (2007). Realisert avkastning på aksjeindeksobligasjoner. Praktisk Økonomi & Finans. ISSN 1501-0074. p. 75–87. Full text in Research Archive
• Koekebakker, Steen & Zakamouline, Valeri (2007). Historisk Avkastning på Garanterte Spareprodukter. Praktisk Økonomi & Finans. ISSN 1501-0074. 4. Full text in Research Archive Show summary

  I denne artikkelen undersøker vi historisk avkastning på garanterte spareprodukter. Risikoen ved slike investeringsprodukter er høyere enn risikofri eksponering, og lavere enn full eksponering mot det underliggende markedet. Dette skulle tilsi en forventet ekstraavkastning utover bankrenten. Resultatet er totalt sett nedslående. Realisert avkastning for garanterte spareprodukter over en 10-årsperiode ligger klart under bankrenten.

• Zakamouline, Valeri (2007). Skewness Preferences in Investment Decisions. Full text in Research Archive
• Zakamouline, Valeri (2007). Can we measure portfolio performance? Full text in Research Archive
• Zakamouline, Valeri (2006). Hedging of Option Portfolios with Transaction Costs and Nonlinear Partial Differential Equations. Full text in Research Archive
• Koekebakker, Steen & Zakamouline, Valeri (2006). Forventet Avkastning på Aksjeindeksobligasjoner. Praktisk Økonomi & Finans. ISSN 1501-0074. 4, p. 75–87. Full text in Research Archive Show summary

  Aksjeindeksobligasjoner er blitt en populær spareform i Norge, og mange velger å lånefinansiere slike investeringer. Hovedgrunnen til populariteten er utvilsomt at tapspotensialet er begrenset og at flere finansinstitusjoner har brukt store ressurser på markedsføring av produktene. Det har frem til nå vært svært lite fokus på gevinstpotensialet til disse produktene. I denne artikkelen forklarer vi hvordan vi kan beregne forventet avkastning på aksjeindeksobligasjoner. Vi eksemplifiserer med to produkter som ble lansert av DnB høsten 2000. Selv med optimistiske antagelser om forventet avkastning i aksjemarkedet, viser det seg at forventet avkastning på disse produktene så vidt overstiger risikofri rente. Ved lånefinansiering finner vi at kundene har negativ forventet avkastning

• Zakamouline, Valeri (2006). Optimal Dynamic Hedging of Options and Option Portfolio in the Presence of Transaction Costs. Full text in Research Archive
• Zakamouline, Valeri (2006). On the Irrelevance of Expected Stock Returns in the Pricing of Options in the Binomial Model. A Pedagogical Note. ?. 3(2), p. 20–31. Full text in Research Archive Show summary

  The option pricing theory is now either a standard or a main part of many financial courses on both intermediate and advanced levels. Despite lots of textbooks written on the pricing of options, teaching a course on option pricing is not an easy task. The major reason for this is that the option pricing theory produces surprising and counter-intuitive results: the option price does not depend neither on the investors' preferences nor on the expected returns of the underlying stock. The challenge for the instructor of such a course is to explain clearly and carefully why it is so. While the independence of the option price from the investors' preferences can be easily deduced from the absence of arbitrage argument, the independence of the option price from the expected returns of the underlying stock is not so easy to explain. Surprisingly, to the best of our knowledge, we have not seen a single textbook that emphasizes and clarifies this matter. Consequently, the main purpose of this paper is to demonstrate the irrelevance of the expected stock returns in the pricing of options in both the continuous time and binomial models. The emphasize is given to the binomial model which, although quite simple and intuitive in appearance, does create some confusions when it comes to its practical implementations and applications.

• Zakamouline, Valeri (2006). Dynamic Hedging of Complex Option Positions with Transaction Costs. Full text in Research Archive
• Zakamouline, Valeri (2006). Yet Another Note on the Leland's Option Hedging Strategy with Transaction Costs. Wilmott Magazine. ISSN 1540-6962. March 2006, p. 70–78. Full text in Research Archive Show summary

  In a market with transaction costs the option hedging is costly. The idea presented by Leland (1985) was to include the expected transaction costs in the cost of a replicating portfolio. The resulting Leland's pricing and hedging method is an adjusted Black-Scholes method where one uses a modified volatility in the Black-Scholes formulas for the option price and delta. The Leland's method has been criticized on different grounds. Despite the critique, the risk-return tradeoff of the Leland's strategy is often better than that of the Black-Scholes strategy even in the case when a hedger starts with the same initial value of a replicating portfolio. This implies that the Leland's modification of volatility does optimize somehow the Black-Scholes hedging strategy in the presence of transaction costs. In this paper we explain how the Leland's modified volatility works and show how the performance of the Leland's hedging strategy can be improved by finding the optimal modified volatility. It is not claimed that the Leland's hedging strategy is optimal. Rather, the optimization mechanism of the modified hedging volatility can be exploited to improve the risk-return tradeoffs of other well-known option hedging strategies in the presence of transaction costs.

• Zakamouline, Valeri (2009). The Choice of Performance Measure Does Influence the Evaluation of Hedge Funds. Universitetet i Agder. Full text in Research Archive
• Zakamouline, Valeri (2009). Portfolio Performance Evaluation with Loss Aversion. Universitetet i Agder. Full text in Research Archive
• Zakamouline, Valeri (2009). Sharpe (Ratio) Thinking About the Investment Opportunity Set and CAPM Relationship. Universitetet i Agder. Full text in Research Archive
• Zakamouline, Valeri (2006). Optimal Hedging of Option Portfolios with Transaction Costs. Universitetet i Agder. Full text in Research Archive
• Zakamouline, Valeri (2006). Hedging of Option Portfolios with Transaction Costs and Nonlinear Partial Differential Equations. Universitetet i Agder. Full text in Research Archive
• Koekebakker, Steen & Zakamouline, Valeri (2006). Forventet Avkastning på Aksjeindeksobligasjoner. Universitetet i Agder. Full text in Research Archive
• Zakamouline, Valeri (2006). On the Pricing and Hedging of Options on Commodity Forward and Futures Contracts. Universitetet i Agder. Full text in Research Archive

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